Homogeneous Diophantine approximation in S-integers

Edward Burger

Vol. 152 (1992), No. 2, 211–253

DOI: 10.2140/pjm.1992.152.211

Abstract

In this paper we generalize classical results in Diophantine approximation to the setting of an arbitrary numher field in the context of the ring of S-integers. Specifically, we present theorems pertaining to simultaneous approximations of linear forms and develop the notion of badly approximable S-systems. In addition, we expand the subject of the geometry of numbers over the adèle ring of a number field by developing the concept of the adelic polar body. This theory is then used to produce transference theorems in this general situation.

Mathematical Subject Classification 2000

Primary: 11J13

Secondary: 11J25, 11R56

Milestones

Received: 23 March 1990

Published: 1 February 1992